There's a lot of really good stuff out there, but a lot of it is from older bands. If you haven't listened to any of the stuff by the classics (The Beatles, Rolling Stones, Who, etc.), I'd strongly suggest it. If you want a more modern sound though, and you want bands who are still together, try these.
Bishop Allen
A great band from Brooklyn who are writing very catchy songs with great lyrics. If you want to get a taste of what they're like, get these songs: Flight 180 and The Ancient Common Sense of Things
The Polyphonic Spree
An aquired taste in music, combining symphonic rock, electronica, r&b and experimental. Recommended first listenings: The Championship, Hanging Around the Day Part II and Hold Me Now
Josh Ritter
A folk singer/songwriter with a very unique sound for his genre. Writes funny but powerful songs, and I much prefer his newer stuff. Suggested listening: Wolves and To The Dogs or Whoever
Jonathan Coulton
He writes songs that have wonderful instrumentation... and he has a very, very, very dry sense of humor. Suggested listening: Thing a Week 2 (It's a whole album, totally free from his website, but you really should pay for it if you like it enough, because that's the only money he makes)
I will also include a list of songs I suggest to anybody who asks of me my music preference. Here they are...
Song - Artist
The Championship - The Polyphonic Spree
While My Guitar Gently Weeps - The Beatles
Band on the Run - Wings
All Along the Watchtower - Jimi Hendrix band
Double Violin Concerto - J.S. Bach
London Calling - The Clash
Armchair Apocrypha - Andrew Bird
Kelly's Blues - Wynton Kelly
Tribute - Tenacious D
Imagine - John Lennon
Penguins - Lyle Lovett
Tonight You Belong to Me - Patience and Prudence
Don't Stop Believin' - Journey
Flight 180 - Bishop Allen
To the dogs or whoever - Josh Ritter
Prelude/Angry Young Man - Billy Joel
Fa-fa-fa - Datarock
Watch Me Now - Arrested Development
Myriad Harbour - The New Pornographers
Walking on the Moon - The Police
You Can Count on Me - Spyro Gyra
Holiday - Green Day
I Know Your Name - Lemon Demon
Remember, if you want real good music start listening to THE BEATLES!!!!! They are probably the second greatest musical entity of the 20th century, only topped by miles davis, in their scope, popularity and musical ability. Best beatles albums... Start with Rubber Soul and Revolver.